%0 Journal Article
%T A Revision of <i>AIC</i> for Normal Error Models
%A Kunio Takezawa
%J Open Journal of Statistics
%P 309-312
%@ 2161-7198
%D 2012
%I Scientific Research Publishing
%R 10.4236/ojs.2012.23038
%X Conventional Akaike¡¯s Information Criterion (<i>AIC</i>) for normal error models uses the maximum-likelihood estimator of error variance. Other estimators of error variance, however, can be employed for defining <i>AIC</i> for normal error models. The maximization of the log-likelihood using an adjustable error variance in light of future data yields a revised version of <i>AIC</i> for normal error models. It also gives a new estimator of error variance, which will be called the ¡°third variance¡±. If the model is described as a constant plus normal error, which is equivalent to fitting a normal distribution to one-dimensional data, the approximated value of the third variance is obtained by replacing (n-1) (n is the number of data) of the unbiased estimator of error variance with (n-4). The existence of the third variance is confirmed by a simple numerical simulation.
%K &lt
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%K AIC&lt
%K /i&gt
%K &lt
%K i&gt
%K AIC&lt
%K sub&gt
%K c&lt
%K /sub&gt
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%K /i&gt
%K Normal Error Models
%K Third Variance
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=20651